Thermal States and Wave Packets

TL;DR

This paper derives a method to connect classical and quantum descriptions of thermal equilibrium for non-interacting particles using convex decompositions into wave packets, bridging the gap between localized and delocalized states.

Contribution

It introduces a convex decomposition of thermal states into wave packets, linking classical phase space distributions with quantum energy eigenstates for non-interacting particles.

Findings

Wave packet distributions correspond to classical thermal states.

The decomposition captures quantum statistics of fermions and bosons.

Provides a unified framework for classical-quantum thermal descriptions.

Abstract

The classical and quantum representations of thermal equilibrium are strikingly different, even for free, non-interacting particles. While the first involves particles with well-defined positions and momenta, the second usually involves energy eigenstates that are delocalized over a confining volume. In this paper, we derive convex decompositions of the density operator for non-interacting, non-relativistic particles in thermal equilibrium that allow for a connection between these two descriptions. Associated with each element of the decomposition of the N-particle thermal state is an N-body wave function, described as a set of wave packets; the distribution of the average positions and momenta of the wave packets can be linked to the classical description of thermal equilibrium, while the different amplitudes in the wave function capture the statistics relevant for fermions or bosons.